The Decibel
Basic Decibels The decibel is based on the logarithm of the ratio between two numbers. It describes how much larger or smaller one value is than the other. It can also be used as an absolute unit of measurement if the reference value is fixed and known. Some standardized references have been estab- lished for decibel scales in different fields of sound engi- neering (see below). The decibel is strictly ten times the logarithm to the base ten of the ratio between the powers of two signals: dB=10log (P''/''P) 10 1 2 For example, the difference in decibels between a signal with a power of 1 watt and one of 2 watts is 10log(2/1) = 3dB. If the decibel is used to compare values other than signal powers, the relationship to signal power must be taken into account. Voltage has a square relationship to power (from Ohm’s law: W ''= ''V ''2/''R); thus to compare two voltages: dB = 10 log(V''12/''V''22), or 10 log(''V''1/''V''2)2, or 20log(''V''1/''V''2) For example, the difference in decibels between a signal with a voltage of 1 volt and one of 2 volts is 20log(2/1) = 6dB. So a doubling in voltage gives rise to an increase of 6dB, and a doubling in power gives rise to an increase of 3dB. A similar relationship applies to acoustical sound pressure (analogous to electrical volt- age) and sound power (analogous to electrical power). '''Decibels with a Reference' If a signal level is quoted in decibels, then a reference must normally be given, otherwise the figure means noth- ing; e.g. ‘Signal level = 47 dB’ cannot have a meaning unless one knows that the signal is 47dB above a known point. ‘ +8 dB ref. 1 volt’ has a meaning since one now knows that the level is 8dB higher than 1 volt, and thus one could calculate the voltage of the signal. There are exceptions in practice, since in some fields a reference level is accepted as implicit. Sound pressure levels (SPLs) are an example, since the reference level is defined worldwide as 2 X 10-5 N m-2 (20 μPa). Thus to state ‘SPL = 77 dB’ is probably acceptable, although con- fusion can still arise due to misunderstandings over such things as weighting curves (see Fact File 1.4). In sound recording, 0dB or ‘zero level’ is a nominal reference level used for aligning equipment and setting recording levels, often corresponding to 0.775 volts (0dBu) although this is subject to variations in studio centers in different loca- tions. (Some studios use 4dBu as their reference level, for example.) ‘0dB’ does not mean ‘no signal’, it means that the signal concerned is at the same level as the reference. Often a letter is placed after ‘dB’ to denote the refer- ence standard in use (e.g. ‘dBm’), and a number of standard abbreviations are in use, some examples of which are given below. Abbrev. Ref. level dBV 1 volt dBu 0.775 volt (Europe) dBv 0.775 volt (USA) dBm 1 milliwatt Useful Decibel Ratios to Remember (Voltages or SPLs) It is more common to deal in terms of voltage or SPL ratios than power ratios in audio systems. Here are some useful dB equivalents of different voltage or SPL relation- ships and multiplication factors: dB Multiplication factor 0 1 +3 '√'2 ' '+6 2 ' '+20 10 +60 1000